Steps toward the weak higher category of weak higher categories in the globular setting (Q2834672)

The author proposed in [Cah. Topol. Géom. Différ. Catég. 52, No. 4, 269--316 (2011; Zbl 1258.18003); correction ibid. 54, No. 1, 75--80 (2013)] a definition of higher operads that should capture the essence of weak higher transformations between Batanin's higher categories. These operads contain however so many coherence conditions that some fairly simple natural transformations cannot be algebras over these higher operads. The present article proposes a corrected version of these higher operads \(B^n_C\), extending Batanin's \(B^0_C\), as well as a strict analogue. The final section introduces the conjecture that \(B^0_C\) should be fractal. A positive answer to this conjecture would have implications about the existence of the globular weak higher category of globular weak higher categories. The strict analogue of this conjecture is also open, even though the strict analogous consequence is known to be true.